Stats Vocab - Chapter 1

Quantitative

Quantity - Numbers

Qualitative

Qualities - Words / No mathematical value

Continuous data

Data you can measure, like height, weight, temperature, or time.

You can get decimal values (e.g., 5.7 cm, 98.6°F), and there are infinite possibilities between any two values

Discrete

Countable (whole numbers only)

Fx: 3 kids, 10 pencils, 25 students

Nominal

Aka: Categorical

Name-only / Used to classify or group things

FX: Eye color (blue, green, brown)

Type of fruit (apple, banana, orange)

Gender (male, female, nonbinary)

Zip code (just a label, not a value)

Ordinal or Rank

Shows which comes first, second, third, etc. - but doesn’t tell you how much better or worse one is from the other

Fx: Ranked choice voting

Fx2:

Survey answers: "Strongly agree," "Agree," "Neutral," "Disagree"

T-shirt sizes: Small, Medium, Large

Contest results: 1st place, 2nd place, 3rd place

Military ranks: Private, Corporal, Sergeant

A variable

Something that varies from individual to individual in your dataset — for example, each person has a different age or height

An individual

Any person, animal or thing described in a set of data

A variable is

Any attribute that can take different values for different individuals

Categorical

No math numbers

Can still be number but used as a group. Like were you born in the 80s or 90s. Or what year a movie came out

2-4, 10-19

Categorical
-Because you can’t do meaningful math with them

2, 10, 19, 30

Quantitative
-Because you can calculate averages and add and subtract them in formulas

Inference

To draw conclusions about a population based on simple data

Order or Rank Data

Data that has a clear order or ranking, but the differences between the values are not exact or evenly spaced

Ex: 1st place, 2nd place, 3rd place (we know the order, but not how much faster one was than the other)

"Very satisfied," "Satisfied," "Neutral," "Dissatisfied," "Very dissatisfied"

Interval data

Numerical data where the order matters and the differences between values are meaningful and equal, but there is no true zero

Fx: Temperature in Celsius or Fahrenheit

(20°C is hotter than 10°C, and the difference is 10 degrees—but 0°C doesn’t mean “no temperature”)

Dates on a calendar (e.g., the year 2000 vs. 2010)

What the heck is year 0
The guys who invented ferenhiet was 32 when he invented it

Ratio data

The order matters

The differences are meaningful

There is a true zero — which means none of the quantity is present

You can add, subtract, multiply, and divide

Fx: Weight (0 kg means no weight)

Height (0 cm means no height)

Money ($0 means no money)

Time (0 seconds = no time passed)

🧠 Key Idea:

You can say things like “twice as much” or “half as long.”

Nonresponse bias

People in the sample did not reply

Undercoverage bias

The sample itself misses key parts of the population

Multicenter study

Cluster study = Same

Observational study

When researchers watch and record what happens without interfering or changing anything. (Observe subjects in their natural setting)

Experimental study

When researchers actively change something (apply a treatment) and measure the results

Fx: Researchers assign groups (e.g., treatment vs. control), control variables. They can show cause and effect

Cross-sectional study

Snapshot study. Looks at data from a group of people at one single point in time — like a snapshot

Retrospective study

Looks backward in time — it uses past data to find patterns or connections

Prospective (aka Longitudinal) study

A __________ study looks forward in time — researchers start now and follow people into the future to see what happens.

"Start now, watch what happens later."

Confounding

Occurs when two variables are associated in such a way that their effects on a response variable cannot be distinguished from each other

A __________ variable is a hidden or third variable that:

Affects both the independent variable

Blocks

Subjects are grouped into blocks based on something they have in common (like age, gender, or location)

"Group first, then randomize — apples with apples, oranges with oranges."

Random sample

A way of picking people or items by chance, so the choice isn’t biased. - Several mini buckets. You go to 4 random classrooms and pick 2 students from each.

Still random, but not everyone in the school had the same chance. Some classes could have 30 students while others 10 students.

Simple random sample

A type of random sample where everyone has the same chance of being picked. - One big hat. You write all 100 names on slips of paper, put them in a hat, mix well, and draw 10 names.

Probability sample

Means any sampling method where each person has a known chance of being selected

Fx: This includes random sampling, stratified sampling, cluster sampling, etc.

Systematic sampling

Picking every kth person from a list after choosing a random starting point.

Fx: Like picking every 5th name on a list, starting at a random spot.

Convenience sampling

Consists of individuals from the population who are easy to reach

Multi-stage sampling

Uses more than one step or method to select the sample — like combining clusters and random sampling

Self-response or Volunteer sampling

Consists of people who choose to be in a sample by responding to a general invitation

Stratified sampling

Divide the population into groups (strata) that share something in common — and then randomly select people from each group.

Fx: A researcher wants to survey 100 college students.

The college is 70% undergrads and 30% grad students.

So they randomly select 70 undergrads and 30 grad students

Cluster sampling

When you split the population into groups — then randomly pick some whole clusters and survey everyone in them.

Measurement errors

Mistakes or differences between the true value and what you actually record or observe. “Wrong number by accident.”

Often more subjective, “ Do you not not like abortion?” Subjective and the question is guided, leading to bias.

Sampling errors

You survey 100 students and 60% like pizza. But if you asked all 1,000 students, maybe only 55% do. That 5% difference is the _____________.

The difference between the result from your sample and the real result from the whole population. “Close, but not exact — because it's just a sample.”

Logic errors

Mistakes in how you think about or set up your study — leading to wrong conclusions. “The method or reasoning is flawed.”

Fx: New Coke example

Precision errors

When your measurements are not consistent or repeatable — the values jump around even if nothing changes. “All over the place.”

You weigh yourself 3 times in a row and get:

150 lbs, 154 lbs, 148 lbs.

The scale has ________ error — it's not giving consistent results.

Reliability error

When a measurement tool doesn’t give consistent results every time you use it.

“It gives different answers even if nothing has changed.”

=Not repeatable

Validity

How well a test or method measures what it’s supposed to measure. “Are we measuring the right thing?”

You want to measure math skills, but your test mostly checks reading — it’s not valid.

Even if people get consistent scores (reliable), the test doesn’t measure the right thing — so it’s not valid.

Accuracy

How close your result or measurement is to the true value

Accuracy error

When your measurement is consistently off from the true value — even if it's always the same.

✅ You hit the same spot every time, but it’s the wrong spot.

Example:

If a scale always says 120 lbs when the true weight is 130 lbs, it’s accurate error — it’s off by 10 lbs every time.

Validity error

When your measurement doesn’t actually measure what it’s supposed to measure.

✅ You're measuring something — just not the right thing.

Uncertainty versus Variability

Variability = Natural differences in the world

Uncertainty = How sure we are about our conclusions

“Variability is in the data; uncertainty is in the knowledge.”

Measurements versus numbers

"Measurements have error; numbers have differences."

Measurements

Values taken using a tool or process to quantify something (like weight, height, temperature).

Often associated with: Uncertainty because tools and techniques aren’t perfect.

Example: A thermometer reads 98.4°F — but is it exactly that? Maybe not.

Numbers (Data Values)

The actual values or observations recorded (could come from measurement or counts).

Often associated with: Variability when you’re comparing different data points.

Example: Five people have incomes of $40K, $50K, $55K, $70K, and $90K — those differences show variability.

Stages statistical studies

PPDAC (Planned Parenthood Die All Conservatives)

(Problem) · Step 2 (Plan) · Step 3 (Data) · Step 4 (Analysis) · Step 5 (Conclusion)

Goals of statistical studies

1. Ask a Question

Identify a research question or objective

2. Plan the Study

Design the study / Decide what data to collect

3. Collect the Data

Gather data / Conduct the study

4. Analyze the Data

Summarize and make sense of the data

5. Draw Conclusions

Interpret the results / Make inferences

Strata

Groups of individuals in a population that share characteristics thought to be associated with the variables being measured in a study